Assesment of dispersion and standard deviation

Verification of the dispersion

Compare the involved period’s standard deviation (s) with the corresponding value (s_tot) for all prior observations.

Verify based on the criterion:

Where:

F(0.975;n – 1, n_tot – 1) is the value of the F test for a probability α = 0.025 with n observations or s and n_tot observations of s_tot.

The criterion is based on a single-sided F test with a probability of α = 0.025. For n = 30 and 100 observations for s_tot F equals 1.72.

You can calculate

= FINV( 0,025; n-1; ntot-1)

FINC is replaced by F.INV. The probability is 0,975.

Verification of the central value

The mean () of the involved period is compared with the matching value (_tot) for all prior observations.

Verify based on the criterion:

Where:

x        – Is the mean for the relevant period
x tot   – Is the mean for a consecutive period up to the relevant period
s         – Is the standard deviation for the relevant period
s tot   – Is the standard deviation for a consecutive period up to the relevant period
n        – Is the total number of observations in the relevant period
n  tot  – Is the total number of prior observations

If the relevant criterion is met, the values of the involved period are added together with the ones of the consecutive period up to the involved period for the continuation chart.
If the criterion is not met, start an investigation into the cause.